PI-Net: A Deep Learning Approach to Extract Topological Persistence Images

Som, Anirudh; Choi, Hyung Do; Ramamurthy, Karthikeyan Natesan; Buman, Matthew P.; Turaga, Pavan

doi:10.1109/cvprw50498.2020.00425

Cited by 19 publications

(7 citation statements)

References 33 publications

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“…To the best of our knowledge, we are the first to directly estimate EPDs on graphs with deep learning models. We note that our method is fundamentally different from previous works learning to directly approximate persistence images, a vectorization of persistence diagrams (Som et al, 2020;Montufar et al, 2020). These methods fail to simulate the computation algorithm closely.…”

Section: Introductionmentioning

confidence: 80%

“…Its strategy is to first predict the EPD, and then convert it into the persistence image. To show the superiority of the strategy, we compare with the strategy from (Som et al, 2020;Montufar et al, 2020), i.e., directly approximate the persistence image of the input graph, as a baseline strategy. GIN PI and GAT PI denote the baseline strategy with GIN (Xu et al, 2018) and GAT (Veličković et al, 2018) as the backbone GNNs.…”

Section: Approximation Qualitymentioning

confidence: 99%

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Neural Approximation of Graph Topological Features

Yan¹,

Ma²,

Gao³

et al. 2022

Preprint

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Persistent homology is a widely used theory in topological data analysis. In the context of graph learning, topological features based on persistent homology have been used to capture potentially high-order structural information so as to augment existing graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs, especially since in learning applications one has to carry out this computation potentially many times. Inspired by recent success in neural algorithmic reasoning, we propose a novel learning method to compute extended persistence diagrams on graphs. The proposed neural network aims to simulate a specific algorithm and learns to compute extended persistence diagrams for new graphs efficiently. Experiments on approximating extended persistence diagrams and several downstream graph representation learning tasks demonstrate the effectiveness of our method. Our method is also efficient; on large and dense graphs, we accelerate the computation by nearly 100 times.

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Section: Introductionmentioning

confidence: 80%

Section: Approximation Qualitymentioning

confidence: 99%

Neural Approximation of Graph Topological Features

Yan¹,

Ma²,

Gao³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Importantly, they provide guarantees of the differentiability of PLLAY with respect to the layer's input: hence, such a layer may be placed anywhere in the network. In [64] it is demonstrated how to fuse persistence image computation in supervised deep learning architectures: PI-Net is maybe the first framework using deep learning for computing topological features directly from data. Authors tested such framework on two applications: human activity recognition using tri-axial accelerometer sensor data and image classification.…”

Section: Topological Layersmentioning

confidence: 99%

Learning Topology: Bridging Computational Topology and Machine Learning

Moroni

Pascali

2021

Pattern Recognit. Image Anal.

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Topology is a classical branch of mathematics, born essentially from Euler's studies in the XVII century, which deals with the abstract notion of shape and geometry. Last decades were characterized by a renewed interest in topology and topology-based tools, due to the birth of computational topology and Topological Data Analysis (TDA). A large and novel family of methods and algorithms computing topological features and descriptors (e.g. persistent homology) have proved to be effective tools for the analysis of graphs, 3d objects, 2D images, and even heterogeneous datasets. This survey is intended to be a concise but complete compendium that, offering the essential basic references, allows you to orient yourself among the recent advances in TDA and its applications, with an eye to those related to machine learning and deep learning.

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“…Garin et al [15] use persistent features from different filtration functions and representations to classify hand-written digits. Generating approximate PIs using a deep neural network has also been explored for image classification [16].…”

Section: Introductionmentioning

confidence: 99%

Visual Object Recognition in Indoor Environments Using Topologically Persistent Features

Samani,

Yang,

Banerjee

2020

Preprint

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Object recognition in unseen indoor environments remains a challenging problem for visual perception of mobile robots. In this letter, we propose the use of topologically persistent features, which rely on the shape information of the objects, to address this challenge. In particular, we extract two kinds of features, namely, sparse persistence image (PI) and amplitude, by applying persistent homology to multi-directional height function-based filtrations of the cubical complexes representing the object segmentation maps. The features are then used to train a fully connected network for recognition. For performance evaluation, in addition to a widely-used shape dataset, we collect a new dataset comprising scene images from two different environments, namely, a living room and a mock warehouse. The scenes in both the environments include up to five different objects that are chosen from a given set of fourteen objects. The objects have varying poses and arrangements, and are imaged under different illumination conditions and camera poses. The recognition performance of our methods, which are trained using the living room images, remains relatively unaffected on the unseen warehouse images. In contrast, the performance of the state-of-the-art Faster R-CNN method decreases significantly. In fact, the use of sparse PI features yields higher overall recall and accuracy; and, better F1 scores on many of the individual object classes. We also implement the proposed method on a real-world robot to demonstrate its usefulness.

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PI-Net: A Deep Learning Approach to Extract Topological Persistence Images

Cited by 19 publications

References 33 publications

Neural Approximation of Graph Topological Features

Neural Approximation of Graph Topological Features

Learning Topology: Bridging Computational Topology and Machine Learning

Visual Object Recognition in Indoor Environments Using Topologically Persistent Features

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